TeX джерело:

\begin{array}{l}{5^{2x - 1}} - {5^{2x}} + {2^{2x}} + {2^{2x + 2}} = 0;\;{2^{2x}} + {2^{2x + 2}} = {5^{2x}} - {5^{2x - 1}};\;{2^{2x}}(1 + {2^2}) = {5^{2x}}(1 - {5^{ - 1}});\\\;{2^{2x}} \cdot 5 = {5^{2x}} \cdot \frac{4}{5};\;\frac{{{2^{2x}}}}{{{5^{2x}}}} = \frac{4}{{25}};\;{(\frac{2}{5})^{2x}} = {(\frac{2}{5})^2};\;2x = 2;\;x = 1.\end{array}